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jek_recluse [69]
4 years ago
10

Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of bottles

she needs to sell to earn $100.

Mathematics
1 answer:
taurus [48]4 years ago
7 0

Answer:

the answer is b (Barbara's equation did not consider the number of bottles of iced tea.)

Step-by-step explanation:

its math i did years ago its like simple math for me. trust me i know its right

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1) Solve by using the perfect squares method. x2 + 8x + 16 = 0
Bond [772]
1)
x^2+8x+16=0 \\
(x+4)^2=0 \\
x+4=0 \\
\boxed{x=-4}

2)
x^2-5x-6=0 \\
x^2-6x+x-6=0 \\
x(x-6)+1(x-6)=0 \\
(x+1)(x-6)=0 \\
x+1=0 \ \lor \ x-6=0 \\
x=-1 \ \lor \ x=6 \\
\boxed{x=-1 \hbox{ or } x=6}

3)
\hbox{a perfect square:} \\ (x-a)^2=x^2-2xa+a^2 \\ \\ 2xa=20x \\ a=\frac{20x}{2x} \\ a=10 \\ \\ a^2=10^2=100 \\ \\ \hbox{the expression:} \\ x^2-20x+100 \\ \\ \boxed{\hbox{100 should be added to the expression}}

4)
x^2+8x-8=0 \\ \\
a=1 \\ b=8 \\ c=-8 \\ \Delta=b^2-4ac=8^2-4 \times 1 \times (-8)=64+32=96 \\
\sqrt{\Delta}=\sqrt{96}=\sqrt{16 \times6}=4\sqrt{6} \\ \\
x=\frac{-b \pm \sqrt{\Delta}}{2a}=\frac{-8 \pm 4\sqrt{6}}{2 \times 1}=\frac{2(-4 \pm 2\sqrt{6})}{2}=-4 \pm 2\sqrt{6} \\
\boxed{x=-4-2\sqrt{6} \hbox{ or } x=-4+2\sqrt{6}}

5)
2x^2+12x=0 \\
2x(x+6)=0 \\
2x=0 \ \lor \ x+6=0 \\
x=0 \ \lor \ x=-6 \\
\boxed{x=-6 \hbox{ or } x=0}

6)
2x^2-2x-1=0 \\ \\
a=2 \\ b=-2 \\ c=-1 \\ \Delta=b^2-4ac=(-2)^2-4 \times 2 \times (-1)=4+8=12 \\
\sqrt{\Delta}=\sqrt{12}=\sqrt{4 \times 3}=2\sqrt{3} \\ \\
x=\frac{-b \pm \sqrt{\Delta}}{2a}=\frac{-(-2) \pm 2\sqrt{3}}{2 \times 2}=\frac{2 \pm 2\sqrt{3}}{2 \times 2}=\frac{2(1 \pm \sqrt{3})}{2 \times 2}=\frac{1 \pm \sqrt{3}}{2} \\
\boxed{x=\frac{1-\sqrt{3}}{2} \hbox{ or } x=\frac{1+\sqrt{3}}{2}}

7)
x^2-x+2=0 \\ \\
a=1 \\ b=-1 \\ c=2 \\
\Delta=b^2-4ac=(-1)^2-4 \times 1 \times 2=1-8=-7 \\ \\
\boxed{\hbox{the discriminant } \Delta=-7}

8)
3x^2-6x+1=0 \\ \\
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\boxed{\hbox{the discriminant } \Delta=24} \\ \\
\hbox{if } \Delta\ \textless \ 0 \hbox{ then there are no real roots} \\
\hbox{if } \Delta=0 \hbox{ then there's one real root} \\
\hbox{if } \Delta\ \textgreater \ 0 \hbox{ then there are two real roots} \\ \\
\Delta=24\ \textgreater \ 0 \\
\boxed{\hbox{the equation has two real roots}}

9)
y=2x^2+x-3 \\ \\ a=2 \\ b=1 \\ c=-3 \\ \Delta=b^2-4ac=1^2-4 \times 2 \times (-3)=1+24=25 \\ \\ \hbox{the function has two zeros} \\ \boxed{\hbox{the parabola has 2 points in common with the x-axis}} \\ \\ a\ \textgreater \ 0 \hbox{ so the parabola ope} \hbox{ns upwards} \\ \boxed{\hbox{the vertex lies below the x-axis}}

10)
y=x^2-12x+12 \\ \\
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Absolute zero is -459.67 Fahrenheit. How many degrees above absolute zero is the freezing point of water?
grin007 [14]

Answer:

491.67 above

Step-by-step explanation:

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5.How many solutions does the system have?
faust18 [17]

Answer:

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The table shows the results for spinning the spinner 75 times. What is the relative frequency for the event​ "spin a 3​"?
Vadim26 [7]

Answer: 0.267

Step-by-step explanation:

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In this case we have 75 trials.

in 20 trials the outcome was a 3.

Then the relative frequency of the event "spin a 3" is:

p = 20/75 = 0.266... = 0.267

3 0
3 years ago
Which of the following is a factor of 2x^2-3x-2
Savatey [412]
2x^2 - 3x - 2 = (2x + 1)(x - 2)

The factors of 2x^2 - 3x - 2 are 2x + 1 and x - 2.
6 0
3 years ago
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